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Results tagged with reference-request
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user 13767
This tag is used if a reference is needed in a paper or textbook on a specific result.
12
votes
3
answers
2k
views
What is a good introduction to branching rules in representation theory?
I'm looking for a book or introductory article, that explains branching rules in representation theory of real Lie groups.
When a Lie group has a set of irreducible representations, I'd like to know h …
- 5,565
8
votes
0
answers
221
views
Ends and parametricity
It is well known that a set of natural transformations can be expressed as an end:
$$\int_{A \in \mathcal{A}} \mathcal{B}(FA, GA) =_{\operatorname{Set}} \operatorname{Nat}(F, G)$$
This holds for func …
- 5,565
0
votes
Theoretical physics: Why not just $\mathbb{R}^4$?
If you accept that quantum gravity with matter should be a Topological Quantum Field Theory and that TQFTs probably can't distinguish simply connected homotopy equivalent 4-manifolds, you should come …
- 5,565
10
votes
1
answer
773
views
What are Kirby diagrams of candidate exotic 4-manifolds?
It is an open problem whether there exist smooth manifolds homeomorphic, but not diffeomorphic to the standard $S^4$. The same is true for the 4-torus and several other manifolds. Handle decomposition …
- 5,565
9
votes
1
answer
267
views
Is the modularisation of a unitary fusion category always unitary?
Suppose $\mathcal{C}$ is a unitary ribbon fusion category. Also assume that its symmetric centre has trivial twist and trivial pivotal structure, i.e. is tannakian. Thus, the Müger/Bruguières modulari …
- 5,565
8
votes
1
answer
357
views
What's the (monoidal) image of a monoidal functor?
For an ordinary functor $F\colon \mathcal{C} \to \mathcal{D}$ of categories, there is a construction $\operatorname{im} F$, the image of $F$, which is again a category, and $F$ factors through that im …
- 5,565
7
votes
3
answers
890
views
Is the bordism from disjoint union to connected sum universal for connected manifolds?
Let $M_1$ and $M_2$ be two oriented, connected, closed $n$-manifolds. It is known that the disjoint union $M_1 \sqcup M_2$ and the connected sum $M_1 \# M_2$ are cobordant, via a bordism $\Sigma_{M_1, …
- 5,565
3
votes
2
answers
318
views
How well is the classification of low-dimensional semisimple Hopf superalgebras (or braided ...
As far as I know, low-dimensional semisimple Hopf algebras are classified (along with non-semisimple ones) up to dimension 60, with the first example of a semisimple Hopf algebra not coming from a fin …
- 5,565
9
votes
1
answer
639
views
Is Turaev-Viro-Barrett-Westbury stronger than homotopy?
I've heard that Reshetikhin-Turaev (RT) is stronger than homotopy, and it can distinguish certain homotopy-equivalent, but non-homeomorphic Lens spaces (I think $L(7,1)$ and $L(7,2)$). Now the Turaev- …
- 5,565
5
votes
What programming language should a professional mathematician know?
Not so much a programming language in the classical sense, but a graphical language that is still in its baby shoes: Globular. You can define and manipulate some kind of globular higher categories (Ja …